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Abstract

A multiple-scattering Monte Carlo model that can produce near-photographic quality images is developed and used to simulate several dramatic halo displays. The model atmosphere contains an absorbing ozone layer plus two clear, molecular air layers with Rayleigh scattering surrounding a cloud layer and an atmospheric boundary layer with aerosol particles subject to Lorentz–Mie scattering. Halos are produced by right hexagonal or pyramidal crystals that reflect and refract according to geometric optics without diffraction, although “junk” crystals with a pronounced forward-scattering peak but no halo peaks may be included to simulate typical, faint halos. Model parameters include ozone height and content, surface and cloud pressure, cloud optical thickness, crystal shapes, orientations and abundances, atmospheric turbidity, aerosol radius, and albedo. Beams for each wavelength are sorted into small bins as halo beams if they have been scattered once only by a single crystal and otherwise as sky beams, which are smoothed and combined with the halo beams to produce images. Multiple scattering generally vitiates halos, but extremely rare halos, such as Kern’s arc, can be produced if a significant fraction of crystals in optically thick clouds have identical shapes and are highly oriented. Albedo is a model by-product with potential value in climate studies.

References

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